35. 7 ga karrali ikki xonali sonlar nechta?

We need to find the number of two-digit numbers that are multiples of 7.

Two-digit numbers range from 10 to 99.

The smallest two-digit multiple of 7 is \( 7 \times 2 = 14 \).

The largest two-digit multiple of 7 is \( 7 \times 14 = 98 \).

We can find the number of multiples by dividing the largest by 7 and subtracting the number of multiples less than 10. Alternatively, we can use the count of multiples of 7 up to 99 and subtract the count of multiples of 7 up to 9.

Number of multiples of 7 up to 99 = \( \lfloor \frac{99}{7} \rfloor = 14 \)

Number of multiples of 7 up to 9 = \( \lfloor \frac{9}{7} \rfloor = 1 \)

Number of two-digit multiples of 7 = \( 14 - 1 = 13 \)

Alternatively, using the arithmetic sequence formula:

First term = 14, Last term = 98, common difference = 7.

\( 98 = 14 + (n - 1) \times 7 \)

\( 98 - 14 = (n - 1) \times 7 \)

\( 84 = (n - 1) \times 7 \)

\( \frac{84}{7} = n - 1 \)

\( 12 = n - 1 \)

\( n = 12 + 1 \)

\( n = 13 \)

So, there are 13 two-digit numbers that are multiples of 7.

Ответ: 13